In regards to the American bombing strategy in WW2, Eisenhower actually refused to give the go ahead of carpet bombing in support of troops. This was because hundreds of American soldiers in the 9th and 30th divisions were wounded and killed by friendly fire (bombers) when they were trying to force a hole in the German lines after the Normandy Invasion. I don’t believe it was given again until the battle of the bulge... for obvious reasons (hiding panzers) and panic.
Admittedly, I am an Internet junkie and rarely read WW2 books in-depth. The last book I read was five years ago -- Allied invasion of Italy by Antony Beevor, which was a great read by the way. What I meant by carpet bombing was that I will bomb the infrastructure before the troops started to move. I believe before the beachhead was formed in D-day, the Allied bombers (rocket-firing Typhoon, P-47 Thunderbolt) were destroying railways, shooting up key infrastructure. The French Resistance also helped in the effort. This prevents the enemy divisions from immediately converging on the beachheads once formed. Remember at this time, the Germans were unsure where would be the main beachhead. Of course, once your units started to engage the enemy, all strategic bombing should stop. CAS should be used instead.
in regards to HOI4... I agree that it kinda makes no sense to damage the infrastructure because you are hindering your future advance. In order to fix the supply problem you are going to need to fix the surrounding infrastructure which will allow the enemy to dig in, regroup and obviously cause you further problems at a loss of man power and equipment.
This is a fairly good point. Destroying infrastructure does slow down my troops and let enemy time to dig in. But conversely, the enemy will also get less supplies from damaged infrastructure. And if I have prepared a strong panzer spearhead, the entrenched enemy should be of little problem. Not to mention a strong CAS support.